GATE 2026 ES – Question 48
PM concentrations at seven locations are 45,40,55,65,60,35,50 µg/m³. Find their standard deviation in µg/m³,to one decimal place.
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Correct answer: 10 to 11
Explanation
The mean is $(45+40+55+65+60+35+50)/7=50$. Squared deviations sum to $25+100+25+225+100+225+0=700$. Using the sample convention gives $s=\sqrt{700/(7-1)}=10.8012$,rounded **10.8 µg/m³**. If these seven values are treated as the entire population,$\sigma=\sqrt{700/7}=10.0$; the official accepted range 10–11 accommodates both conventions.